1036: Probability & Statistics
|
|
|
- Oliver Norton
- 5 years ago
- Views:
Transcription
1 036: Probablty & Statstcs Lecture 9 Oe- ad Two-Sample Estmato Problems Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-
2 Statstcal Iferece Estmato to estmate the populato parameters Classcal Based o radom sample Bayesa Based o pror subjectve kowledge about the prob. dstrbuto ad radom sample Tests of hypothess a asserto or cojecture cocerg oe or two populatos Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-
3 Ubased Estmator A estmator may ot expect to estmate the exact value of populato parameter But hope that t s ot fall off Ubased estmator A statstc s sad to be ubased f ts samplg dstrbuto has a mea equal to the parameter estmated ˆ E Θ θ θ Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-3
4 Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-4 Show that S s a ubased estmator of the parameter Therefore, ad,,, for However, ] [ S E E E E E E S E K
5 Most Effcet Estmator The oe wth the smallest varace amog all possble ubased estmators of some populato θ s called the most effcet estmator of θ. ubased Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-5
6 Iterval Estmate Eve most effcet ubased estmator ot lkely to estmate exactly correctly. Although accuracy creases wth large samples, o reaso why a pot estmate from a sample should exactly equal the populato parameter. Oe way to hadle ths error s through a terval estmate Example: sample mea 540 Cofdece terval: 50 m 560 ˆ θ L θ ˆ θ U Sce s x /, accuracy should crease wth ad terval se should decrease. Rage of terval dcates accuracy of the pot estmate Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-6
7 Iterpretato of Iterval Estmates If the cofdece terval s θˆ L θ ˆ θ U The probablty that the mea s wth the rage ca be stated as: P ˆ θ θ ˆ θ L U We would state that there s a - 00% cofdece terval of ˆ θ θ ˆ L θ U Ideally, predct arrow rage wth hgh degree of cofdece Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-7
8 Estmatg the Mea The samplg dstrbuto of s cetered at ad / Hece, t s lkely to be a very accurate estmate whe s large P Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-8
9 Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-9 Cofdece Iterval of ; Kow If s the mea of radom sample of se from a populato wth kow varace, a - 00% cofdece terval for s gve by + P P x x + x Ths works well for 30 eve f the populato s ot ormal
10 Example 9. Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-0
11 Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9- Estmato Error Sce x x + If s used as a estmate of, we ca the be - 00% cofdece that the error wll ot exceed x e e Ths specfed the sample se
12 Example 9.3 Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-
13 I case of ukow T S / I real case, the varace s kow But, we have the sample stadard devato S Recall that the Studet s t-dstrbuto s wth - degrees of freedom. T S / Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-3
14 Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-4 Cofdece Iterval of ; ukow If ad s are the mea ad std. dev. of a radom sample of se from a ormal populato wth ukow varace, a - 00% cofdece terval for s gve by + t S t S P t S t P t s x t s x + x t / s the t-value wth ν- degrees of freedom, leavg a area of / to the rght Replace ormal by t-dstrbuto Replace by S
15 Large Sample Cofdece Iterval If 30, oe ca use ormal dstrbuto stead of Studet s t-dstrbuto, eve whe ormalty caot be assumed. Ths s reasoable because of cetral lmt theorem Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-5
16 Example 9.4 x Prob. & Stat. Lecture09 - oe-/two-sample estmato cwlu@tws.ee.ctu.edu.tw 9-6
Probability and Statistical Methods. Chapter 8 Fundamental Sampling Distributions
Math 3 Probablty ad Statstcal Methods Chapter 8 Fudametal Samplg Dstrbutos Samplg Dstrbutos I the process of makg a ferece from a sample to a populato we usually calculate oe or more statstcs, such as
Probability and Statistical Methods. Chapter 8 Fundamental Sampling Distributions
Math 3 Probablty ad Statstcal Methods Chapter 8 Fudametal Samplg Dstrbutos Samplg Dstrbutos I the process of makg a ferece from a sample to a populato we usually calculate oe or more statstcs, such as
? Economical statistics
Probablty calculato ad statstcs Probablty calculato Mathematcal statstcs Appled statstcs? Ecoomcal statstcs populato statstcs medcal statstcs etc. Example: blood type Dstrbuto A AB B Elemetary evets: A,
Gene Expression Data Analysis (II) statistical issues in spotted arrays
STATC4 Sprg 005 Lecture Data ad fgures are from Wg Wog s computatoal bology course at Harvard Gee Expresso Data Aalyss (II) statstcal ssues spotted arrays Below shows part of a result fle from mage aalyss
Valuation of Asian Option
Mälardales Uversty västerås 202-0-22 Mathematcs ad physcs departmet Project aalytcal face I Valuato of Asa Opto Q A 90402-T077 Jgjg Guo89003-T07 Cotet. Asa opto------------------------------------------------------------------3
Types of Sampling Plans. Types of Sampling Plans. Sampling Procedures. Probability Samples -Simple Random sample -Stratified sample -Cluster sample
Samplg Procedures Defe the Populato Idetfy the Samplg Frame Select a Samplg Procedure Determe the Sample Sze Select the Sample Elemets Collect the Data Types of Samplg Plas o-probablty Samples -Coveece
AMS Final Exam Spring 2018
AMS57.1 Fal Exam Sprg 18 Name: ID: Sgature: Istructo: Ths s a close book exam. You are allowed two pages 8x11 formula sheet (-sded. No cellphoe or calculator or computer or smart watch s allowed. Cheatg
An Efficient Estimator Improving the Searls Normal Mean Estimator for Known Coefficient of Variation
ISSN: 2454-2377, A Effcet Estmator Improvg the Searls Normal Mea Estmator for Kow Coeffcet of Varato Ashok Saha Departmet of Mathematcs & Statstcs, Faculty of Scece & Techology, St. Auguste Campus The
Deriving & Understanding the Variance Formulas
Dervg & Uderstadg the Varace Formulas Ma H. Farrell BUS 400 August 28, 205 The purpose of ths hadout s to derve the varace formulas that we dscussed class ad show why take the form they do. I class we
Consult the following resources to familiarize yourself with the issues involved in conducting surveys:
Cofdece Itervals Learg Objectves: After completo of ths module, the studet wll be able to costruct ad terpret cofdece tervals crtcally evaluate the outcomes of surveys terpret the marg of error the cotext
= 1. UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Parameters and Statistics. Measures of Centrality
UCLA STAT Itroducto to Statstcal Methods for the Lfe ad Health Sceces Istructor: Ivo Dov, Asst. Prof. of Statstcs ad Neurolog Teachg Assstats: Brad Shaata & Tffa Head Uverst of Calfora, Los Ageles, Fall
A Test of Normality. Textbook Reference: Chapter 14.2 (eighth edition, pages 591 3; seventh edition, pages 624 6).
A Test of Normalty Textbook Referece: Chapter 4. (eghth edto, pages 59 ; seveth edto, pages 64 6). The calculato of p-values for hypothess testg typcally s based o the assumpto that the populato dstrbuto
Random Variables. Discrete Random Variables. Example of a random variable. We will look at: Nitrous Oxide Example. Nitrous Oxide Example
Radom Varables Dscrete Radom Varables Dr. Tom Ilveto BUAD 8 Radom Varables varables that assume umercal values assocated wth radom outcomes from a expermet Radom varables ca be: Dscrete Cotuous We wll
Sample Survey Design
Sample Survey Desg A Hypotetcal Exposure Scearo () Assume we kow te parameters of a worker s exposure dstrbuto of 8-our TWAs to a cemcal. As t appes, te worker as four dfferet types of days wt regard to
Review. Statistics and Quantitative Analysis U4320. Review: Sampling. Review: Sampling (cont.) Population and Sample Estimates:
Stattc ad Quattatve Aaly U430 Segmet 6: Cofdece Iterval Prof. Shary O Hallora URL: http://www.columba.edu/tc/pa/u430y-003/ Revew Populato ad Sample Etmate: Populato Sample N X X Mea = = µ = X = N Varace
point estimator a random variable (like P or X) whose values are used to estimate a population parameter
Estimatio We have oted that the pollig problem which attempts to estimate the proportio p of Successes i some populatio ad the measuremet problem which attempts to estimate the mea value µ of some quatity
- Inferential: methods using sample results to infer conclusions about a larger pop n.
Chapter 6 Def : Statstcs: are commoly kow as umercal facts. s a feld of dscple or study. I ths class, statstcs s the scece of collectg, aalyzg, ad drawg coclusos from data. The methods help descrbe ad
Topic-7. Large Sample Estimation
Topic-7 Large Sample Estimatio TYPES OF INFERENCE Ò Estimatio: É Estimatig or predictig the value of the parameter É What is (are) the most likely values of m or p? Ò Hypothesis Testig: É Decidig about
Today: Finish Chapter 9 (Sections 9.6 to 9.8 and 9.9 Lesson 3)
Today: Fiish Chapter 9 (Sectios 9.6 to 9.8 ad 9.9 Lesso 3) ANNOUNCEMENTS: Quiz #7 begis after class today, eds Moday at 3pm. Quiz #8 will begi ext Friday ad ed at 10am Moday (day of fial). There will be
Chapter 10 - Lecture 2 The independent two sample t-test and. confidence interval
Assumptios Idepedet Samples - ukow σ 1, σ - 30 or m 30 - Upooled case Idepedet Samples - ukow σ 1, σ - 30 or m 30 - Pooled case Idepedet samples - Pooled variace - Large samples Chapter 10 - Lecture The
TOPIC 7 ANALYSING WEIGHTED DATA
TOPIC 7 ANALYSING WEIGHTED DATA You do t have to eat the whole ox to kow that the meat s tough. Samuel Johso Itroducto dfferet aalyss for sample data Up utl ow, all of the aalyss techques have oly dealt
Mathematics 1307 Sample Placement Examination
Mathematcs 1307 Sample Placemet Examato 1. The two les descrbed the followg equatos tersect at a pot. What s the value of x+y at ths pot of tersecto? 5x y = 9 x 2y = 4 A) 1/6 B) 1/3 C) 0 D) 1/3 E) 1/6
Inferential Statistics and Probability a Holistic Approach. Inference Process. Inference Process. Chapter 8 Slides. Maurice Geraghty,
Iferetial Statistics ad Probability a Holistic Approach Chapter 8 Poit Estimatio ad Cofidece Itervals This Course Material by Maurice Geraghty is licesed uder a Creative Commos Attributio-ShareAlike 4.0
Estimating the Common Mean of k Normal Populations with Known Variance
Iteratoal Joural of Statstcs ad Probablty; Vol 6, No 4; July 07 ISSN 97-703 E-ISSN 97-7040 Publshed by Caada Ceter of Scece ad Educato Estmatg the Commo Mea of Normal Populatos wth Kow Varace N Sajar Farspour
. (The calculated sample mean is symbolized by x.)
Stat 40, sectio 5.4 The Cetral Limit Theorem otes by Tim Pilachowski If you have t doe it yet, go to the Stat 40 page ad dowload the hadout 5.4 supplemet Cetral Limit Theorem. The homework (both practice
Confidence Intervals Introduction
Cofidece Itervals Itroductio A poit estimate provides o iformatio about the precisio ad reliability of estimatio. For example, the sample mea X is a poit estimate of the populatio mea μ but because of
CHAPTER 8 Estimating with Confidence
CHAPTER 8 Estimatig with Cofidece 8.2 Estimatig a Populatio Proportio The Practice of Statistics, 5th Editio Stares, Tabor, Yates, Moore Bedford Freema Worth Publishers Estimatig a Populatio Proportio
Statistics for Business and Economics
Statistics for Busiess ad Ecoomics Chapter 8 Estimatio: Additioal Topics Copright 010 Pearso Educatio, Ic. Publishig as Pretice Hall Ch. 8-1 8. Differece Betwee Two Meas: Idepedet Samples Populatio meas,
Inferential: methods using sample results to infer conclusions about a larger population.
Chapter 1 Def : Statstcs: 1) are commoly kow as umercal facts ) s a feld of dscple or study Here, statstcs s about varato. 3 ma aspects of statstcs: 1) Desg ( Thk ): Plag how to obta data to aswer questos.
Parametric Density Estimation: Maximum Likelihood Estimation
Parametric Desity stimatio: Maimum Likelihood stimatio C6 Today Itroductio to desity estimatio Maimum Likelihood stimatio Itroducto Bayesia Decisio Theory i previous lectures tells us how to desig a optimal
Introduction to Probability and Statistics Chapter 7
Itroductio to Probability ad Statistics Chapter 7 Ammar M. Sarha, asarha@mathstat.dal.ca Departmet of Mathematics ad Statistics, Dalhousie Uiversity Fall Semester 008 Chapter 7 Statistical Itervals Based
CHAPTER - IV STANDARDIZED CUSUM MEDIAN CONTROL CHART
A Study o Process Varablty usg CUSUM ad Fuzzy Cotrol Charts Ph.D Thess CHAPTER - IV STANDARDIZED CUSUM MEDIAN CONTROL CHART. Itroducto: I motorg e process mea, e Mea ( X ) cotrol charts, ad cumulatve sum
APPENDIX M: NOTES ON MOMENTS
APPENDIX M: NOTES ON MOMENTS Every stats textbook covers the propertes of the mea ad varace great detal, but the hgher momets are ofte eglected. Ths s ufortuate, because they are ofte of mportat real-world
STATIC GAMES OF INCOMPLETE INFORMATION
ECON 10/410 Decsos, Markets ad Icetves Lecture otes.11.05 Nls-Herk vo der Fehr SAIC GAMES OF INCOMPLEE INFORMAION Itroducto Complete formato: payoff fuctos are commo kowledge Icomplete formato: at least
IEOR 130 Methods of Manufacturing Improvement Fall, 2017 Prof. Leachman Solutions to First Homework Assignment
IEOR 130 Methods of Maufacturg Improvemet Fall, 2017 Prof. Leachma Solutos to Frst Homework Assgmet 1. The scheduled output of a fab a partcular week was as follows: Product 1 1,000 uts Product 2 2,000
Chapter 8. Confidence Interval Estimation. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 8, Slide 1
Chapter 8 Cofidece Iterval Estimatio Copyright 2015, 2012, 2009 Pearso Educatio, Ic. Chapter 8, Slide 1 Learig Objectives I this chapter, you lear: To costruct ad iterpret cofidece iterval estimates for
CHAPTER 8. r E( r ) m e. Reduces the number of inputs for diversification. Easier for security analysts to specialize
CHATE 8 Idex odels cgra-hll/ir Copyrght 0 by The cgra-hll Compaes, Ic. All rghts reserved. 8- Advatages of the Sgle Idex odel educes the umber of puts for dversfcato Easer for securty aalysts to specalze
Lecture 4: Parameter Estimation and Confidence Intervals. GENOME 560 Doug Fowler, GS
Lecture 4: Parameter Estimatio ad Cofidece Itervals GENOME 560 Doug Fowler, GS (dfowler@uw.edu) 1 Review: Probability Distributios Discrete: Biomial distributio Hypergeometric distributio Poisso distributio
Supplemental notes for topic 9: April 4, 6
Sta-30: Probablty Sprg 017 Supplemetal otes for topc 9: Aprl 4, 6 9.1 Polyomal equaltes Theorem (Jese. If φ s a covex fucto the φ(ex Eφ(x. Theorem (Beaymé-Chebyshev. For ay radom varable x, ɛ > 0 P( x
Estimating Proportions with Confidence
Aoucemets: Discussio today is review for midterm, o credit. You may atted more tha oe discussio sectio. Brig sheets of otes ad calculator to midterm. We will provide Scatro form. Homework: (Due Wed Chapter
A Coverage Probability on the Parameters of the Log-Normal Distribution in the Presence of Left-Truncated and Right- Censored Survival Data ABSTRACT
Malaysa Joural of Mathematcal Sceces 9(1): 17-144 (015) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Joural homepage: http://espem.upm.edu.my/joural A Coverage Probablty o the Parameters of the Log-Normal
5. Best Unbiased Estimators
Best Ubiased Estimators http://www.math.uah.edu/stat/poit/ubiased.xhtml 1 of 7 7/16/2009 6:13 AM Virtual Laboratories > 7. Poit Estimatio > 1 2 3 4 5 6 5. Best Ubiased Estimators Basic Theory Cosider agai
b. (6 pts) State the simple linear regression models for these two regressions: Y regressed on X, and Z regressed on X.
Mat 46 Exam Sprg 9 Mara Frazer Name SOLUTIONS Solve all problems, ad be careful ot to sped too muc tme o a partcular problem. All ecessary SAS fles are our usual folder (P:\data\mat\Frazer\Regresso). You
Lecture 4: Probability (continued)
Lecture 4: Probability (cotiued) Desity Curves We ve defied probabilities for discrete variables (such as coi tossig). Probabilities for cotiuous or measuremet variables also are evaluated usig relative
Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
B = A x z
114 Block 3 Erdeky == Begi 6.3 ============================================================== 1 / 8 / 2008 1 Correspodig Areas uder a ormal curve ad the stadard ormal curve are equal. Below: Area B = Area
ii. Interval estimation:
1 Types of estimatio: i. Poit estimatio: Example (1) Cosider the sample observatios 17,3,5,1,18,6,16,10 X 8 X i i1 8 17 3 5 118 6 16 10 8 116 8 14.5 14.5 is a poit estimate for usig the estimator X ad
Statistics for Journalism
Statstcs for Jouralsm Fal Eam Studet: Group: Date: Mark the correct aswer wth a X below for each part of Questo 1. Questo 1 a) 1 b) 1 c) 1 d) 1 e) Correct aswer v 1. a) The followg table shows formato
Exam 2. Instructor: Cynthia Rudin TA: Dimitrios Bisias. October 25, 2011
15.075 Exam 2 Istructor: Cythia Rudi TA: Dimitrios Bisias October 25, 2011 Gradig is based o demostratio of coceptual uderstadig, so you eed to show all of your work. Problem 1 You are i charge of a study
MOMENTS EQUALITIES FOR NONNEGATIVE INTEGER-VALUED RANDOM VARIABLES
MOMENTS EQUALITIES FOR NONNEGATIVE INTEGER-VALUED RANDOM VARIABLES MOHAMED I RIFFI ASSOCIATE PROFESSOR OF MATHEMATICS DEPARTMENT OF MATHEMATICS ISLAMIC UNIVERSITY OF GAZA GAZA, PALESTINE Abstract. We preset
Math 124: Lecture for Week 10 of 17
What we will do toight 1 Lecture for of 17 David Meredith Departmet of Mathematics Sa Fracisco State Uiversity 2 3 4 April 8, 2008 5 6 II Take the midterm. At the ed aswer the followig questio: To be revealed
Measures of Dispersion
Chapter IV Meaure of Dpero R. 4.. The meaure of locato cate the geeral magtue of the ata a locate oly the cetre of a trbuto. They o ot etablh the egree of varablty or the prea out or catter of the vual
Lecture 5: Sampling Distribution
Lecture 5: Samplig Distributio Readigs: Sectios 5.5, 5.6 Itroductio Parameter: describes populatio Statistic: describes the sample; samplig variability Samplig distributio of a statistic: A probability
Development of Confidence Interval and Hypothesis Testing for Taguchi Capability Index Using a Bayesian Approach
Iteratoal Joural of Operatos Research Iteratoal Joural of Operatos Research Vol. 3, No., 5675 (6 Develoet of Cofdece Iterval ad Hypothess Testg for Taguch Capablty Ide Usg a Bayesa Approach Shu-Ka S. Fa
COMPARISON OF APPROACHES TO TESTING EQUALITY OF EXPECTATIONS AMONG SAMPLES FROM POISSON AND NEGATIVE BINOMIAL DISTRIBUTION
ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS Volume 66 0 Number 4, 08 https://do.org/0.8/actau08660405 COMPARISON OF APPROACHES TO TESTING EQUALITY OF EXPECTATIONS AMONG SAMPLES
Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring
No-lfe surace mathematcs Nls F. Haavardsso, Uversty of Oslo ad DNB Skadeforskrg Repetto clam se The cocept No parametrc modellg Scale famles of dstrbutos Fttg a scale famly Shfted dstrbutos Skewess No
Lecture 5 Point Es/mator and Sampling Distribu/on
Lecture 5 Poit Es/mator ad Samplig Distribu/o Fall 03 Prof. Yao Xie, yao.xie@isye.gatech.edu H. Milto Stewart School of Idustrial Systems & Egieerig Georgia Tech Road map Poit Es/ma/o Cofidece Iterval
Linear regression II
CS 75 Mache Learg Lecture 9 Lear regresso II Mlos Hauskrecht mlos@cs.ptt.eu 539 Seott Square Lear regresso Fucto f : X Y Y s a lear combato of put compoets f ( w w w w w w, w, w k - parameters (weghts
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Means and Proportions
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Meas ad Proportios Itroductio: I this chapter we wat to fid out the value of a parameter for a populatio. We do t kow the value of this parameter for the etire
BASIC STATISTICS ECOE 1323
BASIC STATISTICS ECOE 33 SPRING 007 FINAL EXAM NAME: ID NUMBER: INSTRUCTIONS:. Write your ame ad studet ID.. You have hours 3. This eam must be your ow work etirely. You caot talk to or share iformatio
0.1 Valuation Formula:
0. Valuatio Formula: 0.. Case of Geeral Trees: q = er S S S 3 S q = er S S 4 S 5 S 4 q 3 = er S 3 S 6 S 7 S 6 Therefore, f (3) = e r [q 3 f (7) + ( q 3 ) f (6)] f () = e r [q f (5) + ( q ) f (4)] = f ()
Poverty indices. P(k;z; α ) = P(k;z; α ) /(z) α. If you wish to compute the FGT index of poverty, follow these steps:
Poverty dces DAD offers four possbltes for fxg the poverty le: - A determstc poverty le set by the user. 2- A poverty le equal to a proporto l of the mea. 3- A poverty le equal to a proporto m of a quatle
ST 305: Exam 2 Fall 2014
ST 305: Exam Fall 014 By hadig i this completed exam, I state that I have either give or received assistace from aother perso durig the exam period. I have used o resources other tha the exam itself ad
Chapter 10 Statistical Inference About Means and Proportions With Two Populations. Learning objectives
Chater 0 Statistical Iferece About Meas ad Proortios With Two Poulatios Slide Learig objectives. Uderstad ifereces About the Differece Betwee Two Poulatio Meas: σ ad σ Kow. Uderstad Ifereces About the
Allocating Risk Dollars Back to Individual Cost Elements
Allocatg Rsk Dollars Back to Idvdual Cost Elemets Stephe A. Book Chef Techcal Offcer MCR, LLC sbook@mcr.com (0) 60-0005 x 0th Aual DoD Cost Aalyss Symposum Wllamsburg VA -6 February 007 007 MCR, LLC Approved
Variance Covariance (Delta Normal) Approach of VaR Models: An Example From Istanbul Stock Exchange
ISSN 2222-697 (Paper) ISSN 2222-2847 (Ole) Vol.7, No.3, 206 Varace Covarace (Delta Normal) Approach of VaR Models: A Example From Istabul Stock Exchage Dr. Ihsa Kulal Iformato ad Commucato Techologes Authorty,
Portfolio Optimization via Pair Copula-GARCH-EVT-CVaR Model
Avalable ole at www.scecedrect.com Systems Egeerg Proceda 2 (2011) 171 181 Portfolo Optmzato va Par Copula-GARCH-EVT-CVaR Model Lg Deg, Chaoqu Ma, Weyu Yag * Hua Uversty, Hua, Chagsha 410082, PR Cha Abstract
A point estimate is the value of a statistic that estimates the value of a parameter.
Chapter 9 Estimatig the Value of a Parameter Chapter 9.1 Estimatig a Populatio Proportio Objective A : Poit Estimate A poit estimate is the value of a statistic that estimates the value of a parameter.
Sampling Distributions & Estimators
API-209 TF Sessio 2 Teddy Svoroos September 18, 2015 Samplig Distributios & Estimators I. Estimators The Importace of Samplig Radomly Three Properties of Estimators 1. Ubiased 2. Cosistet 3. Efficiet I
Chapter 8: Estimation of Mean & Proportion. Introduction
Chapter 8: Estimatio of Mea & Proportio 8.1 Estimatio, Poit Estimate, ad Iterval Estimate 8.2 Estimatio of a Populatio Mea: σ Kow 8.3 Estimatio of a Populatio Mea: σ Not Kow 8.4 Estimatio of a Populatio
Statistics for Economics & Business
Statistics for Ecoomics & Busiess Cofidece Iterval Estimatio Learig Objectives I this chapter, you lear: To costruct ad iterpret cofidece iterval estimates for the mea ad the proportio How to determie
Prediction Error of the Future Claims Component of Premium Liabilities under the Loss Ratio Approach. International Regulatory Changes
Predcto rror o the Future lams ompoet o Premum Labltes uder the Loss Rato Approach (accepted to be publshed ace) AS Aual Meetg November 8 00 Jacke L PhD FIAA Nayag Busess School Nayag Techologcal Uversty
Solutions to Problems
Solutos to Problems ( Pt Pt + Ct) P5-. LG : Rate of retur: rt Pt Basc ($,000 $0,000 + $,500) a. Ivestmet X: Retur.50% $0,000 Ivestmet Y: Retur ($55,000 $55,000 + $6,800).36% $55,000 b. Ivestmet X should
Sampling Distributions and Estimation
Samplig Distributios ad Estimatio T O P I C # Populatio Proportios, π π the proportio of the populatio havig some characteristic Sample proportio ( p ) provides a estimate of π : x p umber of successes
Standard Deviations for Normal Sampling Distributions are: For proportions For means _
Sectio 9.2 Cofidece Itervals for Proportios We will lear to use a sample to say somethig about the world at large. This process (statistical iferece) is based o our uderstadig of samplig models, ad will
Overview. Linear Models Connectionist and Statistical Language Processing. Numeric Prediction. Example
Overvew Lear Models Coectost ad Statstcal Laguage Processg Frak Keller keller@col.u-sb.de Computerlgustk Uverstät des Saarlades classfcato vs. umerc predcto lear regresso least square estmato evaluatg
Chapter 4. More Interest Formulas
Chapter 4 More Iterest ormulas Uform Seres Compoud Iterest ormulas Why? May paymets are based o a uform paymet seres. e.g. automoble loas, house paymets, ad may other loas. 2 The Uform aymet Seres s 0
Density estimation II.
Lecture 5 esty estmato II. Mlos Hausrecht mlos@cs.tt.eu 539 Seott Square Outle Outle: esty estmato: Bomal strbuto Multomal strbuto ormal strbuto oetal famly ata: esty estmato {.. } a vector of attrbute
Sampling Distributions and Estimation
Cotets 40 Samplig Distributios ad Estimatio 40.1 Samplig Distributios 40. Iterval Estimatio for the Variace 13 Learig outcomes You will lear about the distributios which are created whe a populatio is
14.30 Introduction to Statistical Methods in Economics Spring 2009
MIT OpeCourseWare http://ocwmitedu 430 Itroductio to Statistical Methods i Ecoomics Sprig 009 For iformatio about citig these materials or our Terms of Use, visit: http://ocwmitedu/terms 430 Itroductio
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Means and Proportions
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Meas ad Proportios Itroductio: We wat to kow the value of a parameter for a populatio. We do t kow the value of this parameter for the etire populatio because
18.S096 Problem Set 5 Fall 2013 Volatility Modeling Due Date: 10/29/2013
18.S096 Problem Set 5 Fall 2013 Volatility Modelig Due Date: 10/29/2013 1. Sample Estimators of Diffusio Process Volatility ad Drift Let {X t } be the price of a fiacial security that follows a geometric
Elementary Statistics and Inference. Elementary Statistics and Inference. Chapter 20 Chance Errors in Sampling (cont.) 22S:025 or 7P:025.
Elemetary Statistics ad Iferece 22S:025 or 7P:025 Lecture 27 1 Elemetary Statistics ad Iferece 22S:025 or 7P:025 Chapter 20 2 D. The Correctio Factor - (page 367) 1992 Presidetial Campaig Texas 12.5 x
The Statistics of Statistical Arbitrage
Volume 63 Number 5 007, CFA Isttute Robert Ferholz ad Cary Magure, Jr. Hedge fuds sometmes use mathematcal techques to capture the short-term volatlty of stocks ad perhaps other types of securtes. Ths
Introduction to Statistical Inference
Itroductio to Statistical Iferece Fial Review CH1: Picturig Distributios With Graphs 1. Types of Variable -Categorical -Quatitative 2. Represetatios of Distributios (a) Categorical -Pie Chart -Bar Graph
Data Analysis and Statistical Methods Statistics 651
Data Aalyi ad Statitical Method Statitic 65 http://www.tat.tamu.edu/~uhaii/teachig.html Lecture 9 Suhaii Subba Rao Tetig o far We have looked at oe ample hypothei tet of the form H 0 : µ = µ 0 agait H
THE NPV CRITERION FOR VALUING INVESTMENTS UNDER UNCERTAINTY
Professor Dael ARMANU, PhD Faculty of Face, Isurace, Baks ad Stock xchage The Bucharest Academy of coomc Studes coomst Leoard LACH TH CRITRION FOR VALUING INVSTMNTS UNDR UNCRTAINTY Abstract. Corporate
Application of Portfolio Theory to Support Resource Allocation Decisions for Biosecurity
Applcato of Portfolo Theory to Support Resource Allocato Decsos for Bosecurty Paul Mwebaze Ecoomst 11 September 2013 CES/BIOSECURITY FLAGSHIP Presetato outle The resource allocato problem What ca ecoomcs
Notes on Expected Revenue from Auctions
Notes o Epected Reveue from Auctios Professor Bergstrom These otes spell out some of the mathematical details about first ad secod price sealed bid auctios that were discussed i Thursday s lecture You
Chapter 4. More Interest Formulas
Chapter 4 More Iterest ormulas Uform Seres Compoud Iterest ormulas Why? May paymets are based o a uform paymet seres. e.g. automoble loas, house paymets, ad may other loas. 2 The Uform aymet Seres s 0
5 Statistical Inference
5 Statistical Iferece 5.1 Trasitio from Probability Theory to Statistical Iferece 1. We have ow more or less fiished the probability sectio of the course - we ow tur attetio to statistical iferece. I statistical
Lecture 9: The law of large numbers and central limit theorem
Lecture 9: The law of large umbers ad cetral limit theorem Theorem.4 Let X,X 2,... be idepedet radom variables with fiite expectatios. (i) (The SLLN). If there is a costat p [,2] such that E X i p i i=
ATutorialonParticleFilteringandSmoothing: Fifteen years later
ATutoraloPartcleFltergadSmoothg: Fftee years later Araud Doucet The Isttute of Statstcal Mathematcs, 4-6-7 Mam-Azabu, Mato-ku, Tokyo 06-8569, Japa Emal: Araud@smacjp Adam M Johase Departmet of Statstcs,
x satisfying all regularity conditions. Then
AMS570.01 Practice Midterm Exam Sprig, 018 Name: ID: Sigature: Istructio: This is a close book exam. You are allowed oe-page 8x11 formula sheet (-sided). No cellphoe or calculator or computer is allowed.
LECTURE 5: Quadratic classifiers
LECURE 5: Quadratc classfers Bayes classfers for Normally dstrbuted classes Case : σ I Case : ( daoal) Case : ( o-daoal) Case : σ I Case 5: j eeral case Numercal example Lear ad quadratc classfers: coclusos
Topic 14: Maximum Likelihood Estimation
Toic 4: November, 009 As before, we begi with a samle X = (X,, X of radom variables chose accordig to oe of a family of robabilities P θ I additio, f(x θ, x = (x,, x will be used to deote the desity fuctio
Two Approaches for Log-Compression Parameter Estimation: Comparative Study*
SERBAN JOURNAL OF ELECTRCAL ENGNEERNG Vol. 6, No. 3, December 009, 419-45 UDK: 61.391:61.386 Two Approaches for Log-Compresso Parameter Estmato: Comparatve Study* Mlorad Paskaš 1 Abstract: Stadard ultrasoud
ETSI TS V1.2.1 ( )
TS 0 50-6 V.. (004-0) Techcal Specfcato Speech Processg, Trasmsso ad Qualty Aspects (STQ); QoS aspects for popular servces GSM ad 3G etworks; Part 6: Post processg ad statstcal methods TS 0 50-6 V.. (004-0)
8.0% E(R) 6.0% Lend. Borrow 4.0% 2.0% rf rf 0.0% 0.0% 1.0% 2.0% 3.0% 4.0% STD(R) E(R) Long A and Short B. Long A and Long B. Short A and Long B
F8000 Valuato of Facal ssets Sprg Semester 00 Dr. Isabel Tkatch ssstat Professor of Face Ivestmet Strateges Ledg vs. orrowg rsk-free asset) Ledg: a postve proporto s vested the rsk-free asset cash outflow
Glass in building Procedures for goodness of fit and confidence intervals for Weibull distributed glass strength data
Provläsgsexemplar / Prevew SVENSK STANDARD SS-EN 12603 Fastställd 2003-02-07 Utgåva 1 Byggadsglas Förfargssätt vd apassg och kofdestervall för Webullfördelade glashållfasthetsdata Glass buldg Procedures